A cotton reel of mass `m` and moment of inertia `I` is kept at rest on as smooth horizontal surface. The reel has inner and other radius `r` and `R` respectively. A horizontal force `F` starts actings as shown in figure. Find the

a. acceleration of the centre of mass of reel.
b. angular acceleration of the reel
c. net acceleration of point of contact.

Explanation

a. The net force acting on the cotton reel is
`F=ma_(C)`

or `a_(C)=F/m`
b. the net torque about the CM is `tau_(C)(=FR)=Ialpha`
(as torques produced by mg and `N` about `C` are zero as they pass through the `CM`).
Then `alpha=(FR)/I`